Question : The circumference of the base of a cylinder is $28 \pi$ cm. If the height of the cylinder is 17 cm, then what will be the curved surface area of the cylinder?
Option 1: $372 \pi ~\text{cm}^2$
Option 2: $436\pi \ \text{cm}^2$
Option 3: $524\pi \ \text{cm}^2$
Option 4: $476\pi \ \text{cm}^2$
Correct Answer: $476\pi \ \text{cm}^2$
Solution :
Given: The circumference of the base of the cylinder = $28 \pi ~\mathrm{cm}$
We know that,
Circumference of a circle = $2 \pi r$
⇒ $2 \pi r = 28 \pi$
⇒ $r = \frac{28 \pi}{2 \pi} = 14~\mathrm{cm}$
Height of the cylinder = 17 cm
$\therefore$ Curved surface area of the cylinder = $2 \pi r h=2 \times\pi \times 14 \times 17=476\pi~\mathrm{cm}^2$
Hence, the correct answer is $476\pi \ \text{cm}^2$.
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